Current pulse detecting circuits are used for a wide range of applications including sensors which contain a sensing device able to deliver electrical charge representing the sensed physical property. In order to detect minute changes of the sensed physical property, detecting circuits providing a high charge to voltage conversion factor and low noise at high bandwidth are of a major interest.
With reference to FIG. 1, state of the art charge pulse detecting circuits usually comprise a sensing device 101 delivering an amount of charge which represents the sensed physical property to an input node 111, an inverting amplifier 102 and a sense capacitor 103 configured to form a capacitance feedback amplifier, a recharge resistor 104 in parallel with sense capacitor 103 and an input capacitor 105 which may be a parasitic capacitance. For short current pulses delivered by sensing device 101 and high values of recharge resistor 104, amplifier 102 produces on an output node 112 a voltage pulse with a pulse height defined by the integrated charge of the input current pulse and the capacitance value of sense capacitor 103. The input charge is subsequently slowly removed from input node 111 across recharge resistor 104, and a stable DC operation voltage point is established on input node 111 by feedback operation of amplifier 102 and recharge resistor 104. State of the art charge pulse detecting circuits are described in G. Lutz, “Semiconductor Radiation Detectors”, pp. 190, Springer, Berlin; Heidelberg.
Circuit analysis shows that, for the case of an inverting amplifier 102 with a sufficiently high gain-times-bandwidth product, the charge detecting circuit's input current to output voltage transimpedance function may be approximated as:
                                          v            o                                i            in                          ≅                              1            -                          s              ⁢                                                C                  l                                                  gm                  A                                                                                        (                              1                +                                  s                  ⁢                                                                          ⁢                                      R                    r                                    ⁢                                      C                    s                                                              )                        ⁢                          (                              1                +                                  s                  ⁢                                      1                                          gm                      A                                                        ⁢                                      (                                                                  C                        s                                            +                                              C                        i                                            +                                                                                                    C                            l                                                    ⁢                                                      C                            i                                                                                                    C                          s                                                                                      )                                                              )                                                          (        1        )            wherein vo is the ac voltage on output node 112, iin is the ac current delivered by sensing device 101, Cl is a load capacitance connected to output node 112, gmA is the transconductance of amplifier 102, Rr is the resistance value of recharge resistor 104, Cs is the capacitance value of sense capacitor 103, Ci is the sum of capacitance from input node 111 to any ac ground node, and s is the complex signal frequency. Note that alternative mathematical terms may be used to represent the approximation of the transimpedance function.
For frequencies above ½πRrCs but below the zero frequency and the second pole frequency, the transimpedance is approximately equal to 1/sC5 i.e. to the sense capacitance impedance. Therefore, a high charge to voltage conversion factor may be achieved if Cs is small and RrCs is longer than the width of the detected current pulses.
The major noise sources in the discussed state of the art current pulse detecting circuit are amplifier 102 and recharge resistor 104. Noise contributed by amplifier 102 can be arbitrarily reduced by increasing load capacitance, amplifier transconductance and amplifier transistor device area. Circuit analysis under the same assumptions as above yields the following approximation of the output noise power spectral density due to the thermal noise caused by recharge resistor 104:
                              S          Vo                ≅                  4          ⁢                                          ⁢          k          ⁢                                          ⁢                      TR            r                    ⁢                                                                                    1                  +                                      s                    ⁢                                                                                  ⁢                                          C                      i                                        ⁢                                          gm                      A                                                                                                            (                                          1                      +                                              s                        ⁢                                                                                                  ⁢                                                  R                          r                                                ⁢                                                  C                          s                                                                                      )                                    ⁢                                      (                                          1                      +                                              s                        ⁢                                                  1                                                      gm                            A                                                                          ⁢                                                  (                                                                                    C                              l                                                        +                                                          C                              i                                                        +                                                                                                                            C                                  l                                                                ⁢                                                                  C                                  i                                                                                                                            C                                s                                                                                                              )                                                                                      )                                                                                      2                                              (        2        )            
Note that alternative mathematical expressions may be used to represent the approximation of the recharge resistor noise power spectral density. Neglecting the effects of the zero and second pole at high frequency, the input node charge RMS variation qni, Rr, prior art equivalent of the recharge resistor noise can be approximated as:
                              q                      ni            ,                                                  ⁢            Rr            ,                          prior              ⁢                                                          ⁢              art                                      ≅                              kT                          C              s                                                          (        3        )            wherein k is the Boltzmann Constant and T is the absolute temperature in K. Note that different alternative expressions may be used to represent the recharge resistor noise equivalent input charge. We note that low capacitance values of sense capacitor 103 are desirable in order to achieve low detecting circuit noise i.e. high signal to noise ratio at low charge amounts delivered by sensing device 101. There are, however, practical limits to the capacitance value Cs, mainly determined by the constraints of fabrication processes. Therefore, the noise performance of state of the art pulse detecting circuits is limited for a given process technology.